Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, w]$
Label 2.2.456.1-3.1-d
Dimension 6
CM no
Base change no

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Base field \(\Q(\sqrt{114}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[3, 3, w]$
Label 2.2.456.1-3.1-d
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 72

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 23x^{4} \) \(\mathstrut +\mathstrut 152x^{2} \) \(\mathstrut -\mathstrut 236\)

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Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $\phantom{-}0$
3 $[3, 3, w]$ $\phantom{-}1$
5 $[5, 5, w + 2]$ $\phantom{-}e$
5 $[5, 5, w + 3]$ $-e$
7 $[7, 7, -w + 11]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$
7 $[7, 7, w + 11]$ $-\frac{1}{4}e^{4} + \frac{13}{4}e^{2} - \frac{13}{2}$
11 $[11, 11, w + 2]$ $-\frac{1}{8}e^{5} + \frac{17}{8}e^{3} - \frac{29}{4}e$
11 $[11, 11, w + 9]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{17}{8}e^{3} + \frac{29}{4}e$
13 $[13, 13, w + 6]$ $\phantom{-}\frac{3}{8}e^{4} - \frac{43}{8}e^{2} + \frac{47}{4}$
13 $[13, 13, w + 7]$ $\phantom{-}\frac{3}{8}e^{4} - \frac{43}{8}e^{2} + \frac{47}{4}$
19 $[19, 19, w]$ $-\frac{1}{4}e^{4} + \frac{9}{4}e^{2} + \frac{3}{2}$
37 $[37, 37, w + 15]$ $-\frac{1}{8}e^{4} + \frac{25}{8}e^{2} - \frac{53}{4}$
37 $[37, 37, w + 22]$ $-\frac{1}{8}e^{4} + \frac{25}{8}e^{2} - \frac{53}{4}$
41 $[41, 41, 37w + 395]$ $\phantom{-}\frac{1}{8}e^{5} - \frac{9}{8}e^{3} - \frac{3}{4}e$
41 $[41, 41, 5w + 53]$ $-\frac{1}{8}e^{5} + \frac{9}{8}e^{3} + \frac{3}{4}e$
67 $[67, 67, w + 28]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{43}{4}e^{2} + \frac{47}{2}$
67 $[67, 67, w + 39]$ $\phantom{-}\frac{3}{4}e^{4} - \frac{43}{4}e^{2} + \frac{47}{2}$
71 $[71, 71, 40w + 427]$ $\phantom{-}\frac{1}{4}e^{5} - \frac{17}{4}e^{3} + \frac{33}{2}e$
71 $[71, 71, 8w + 85]$ $-\frac{1}{4}e^{5} + \frac{17}{4}e^{3} - \frac{33}{2}e$
73 $[73, 73, -2w + 23]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{11}{2}e^{2} + 3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$